{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# SciPy\n",
    "\n",
    "Examples taken from [Scipy Lecture Notes](http://www.scipy-lectures.org)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Loading default packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import display, Markdown\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "plt.style.use(\"default\")\n",
    "#% matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# plot settings\n",
    "plt.rcParams['figure.figsize'] = [9.5, 4.25]\n",
    "plt.rcParams['figure.dpi'] = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "from scipy import interpolate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Create sample signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "measured_time = np.linspace(0, 1, 10)\n",
    "noise = (np.random.random(10)*2 - 1) * 1e-1\n",
    "measures = np.sin(2 * np.pi * measured_time) + noise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Perform `linear` and `cubic` interpolation with [`interp1d`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "linear_interp = interpolate.interp1d(measured_time, measures)\n",
    "interpolation_time = np.linspace(0, 1, 50)\n",
    "linear_results = linear_interp(interpolation_time)\n",
    "cubic_interp = interpolate.interp1d(measured_time, measures, kind='cubic')\n",
    "cubic_results = cubic_interp(interpolation_time)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Display results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 950x425 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(measured_time, measures, '.-', label='Measured signal')\n",
    "plt.plot(interpolation_time, linear_results, label='Linear interpolation')\n",
    "plt.plot(interpolation_time, cubic_results, label='Cubic interpolation')\n",
    "plt.xlabel('Time $t$ / s')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Fast Fourier transforms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "from scipy import fftpack"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Create a noisy sine signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 950x425 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.arange(0, 10, 0.01)\n",
    "u_t = (np.sin(2 * np.pi * 1 * t) + 0.5 * np.random.randn(t.size))\n",
    "plt.figure()\n",
    "plt.plot(t, u_t)\n",
    "plt.xlabel('Time $t$ / s')\n",
    "plt.ylabel('Voltage $u[t]$ / V')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Compute the Fast Fourier Transformation (real part - positive frequencies)\n",
    "\n",
    "The FFT $U[k]$ of length $N$ of the length-$N$ sequence $u[t]$ is\n",
    "defined as\n",
    "\n",
    "$$X[k] = \\sum_{n=0}^{N-1} e^{-2 \\pi j \\frac{k t}{N} } x[t]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "U_f = fftpack.rfft(u_t)\n",
    "U_f[0] /= u_t.size\n",
    "U_f[1:] /= u_t.size / 2\n",
    "f = fftpack.rfftfreq(u_t.size, 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 950x425 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(f, np.abs(U_f))\n",
    "plt.xlabel('Frequency $f$ / Hz')\n",
    "plt.ylabel('Absolute specturm |U(f)| / V')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Optimization and fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Create noisy data for a function $f(t) = a \\cdot \\sin\\left(b \\cdot t\\right)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 950x425 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_data = np.linspace(-5, 5, num=50)\n",
    "y_data = 2.9 * np.sin(1.5 * x_data) + np.random.normal(size=50)\n",
    "plt.figure()\n",
    "plt.plot(x_data, y_data, '.', label='Measured data')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Create a prototype function for fitting and use [`curve_fit`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$a$ = 2.7654674540755395, $b$ = 1.5008129146800258"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def test_func(x, a, b):\n",
    "    return a * np.sin(b * x)\n",
    "params, params_covariance = optimize.curve_fit(test_func, x_data, y_data, p0=[2, 2])\n",
    "display(Markdown(f'$a$ = {params[0]}, $b$ = {params[1]}'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 950x425 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(x_data, y_data, '.', label='Measured data')\n",
    "plt.plot(x_data, test_func(x_data, params[0], params[1]), label=r'Fitted curve $y(t) = a \\cdot \\sin(b \\cdot t)$')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "RL_course_py12",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
